More Like this

1. Group Fairness via Group Consensus

   https://doi.org/10.1145/3630106.3659006  

   Chan, Eunice; Liu, Zhining; Qiu, Ruizhong; Zhang, Yuheng; Maciejewski, Ross; Tong, Hanghang (June 2024, ACM)
2. Equivariant group presentations and the second homology group of the Torelli group

   https://doi.org/10.1007/s00208-019-01905-5  

   Kassabov, Martin; Putman, Andrew (February 2020, Mathematische Annalen)

   null (Ed.)
3. Optimal orthogonal group synchronization and rotation group synchronization

   https://doi.org/10.1093/imaiai/iaac022  

   Gao, Chao; Zhang, Anderson Y. (August 2022, Information and Inference: A Journal of the IMA)

   Abstract We study the statistical estimation problem of orthogonal group synchronization and rotation group synchronization. The model is $$Y_{ij} = Z_i^* Z_j^{*T} + \sigma W_{ij}\in{\mathbb{R}}^{d\times d}$$ where $$W_{ij}$$ is a Gaussian random matrix and $$Z_i^*$$ is either an orthogonal matrix or a rotation matrix, and each $$Y_{ij}$$ is observed independently with probability $$p$$. We analyze an iterative polar decomposition algorithm for the estimation of $Z^*$ and show it has an error of $$(1+o(1))\frac{\sigma ^2 d(d-1)}{2np}$$ when initialized by spectral methods. A matching minimax lower bound is further established that leads to the optimality of the proposed algorithm as it achieves the exact minimax risk. 

   more » « less
4. Rigid local systems with monodromy group the Conway group Co2

   https://doi.org/10.1142/S1793042120500189  

   Katz, Nicholas M.; Rojas-León, Antonio; Tiep, Pham Huu (March 2020, International Journal of Number Theory)

   null (Ed.)

   We first develop some basic facts about hypergeometric sheaves on the multiplicative group [Formula: see text] in characteristic [Formula: see text]. Certain of their Kummer pullbacks extend to irreducible local systems on the affine line in characteristic [Formula: see text]. One of these, of rank [Formula: see text] in characteristic [Formula: see text], turns out to have the Conway group [Formula: see text], in its irreducible orthogonal representation of degree [Formula: see text], as its arithmetic and geometric monodromy groups. 

   more » « less
5. Group-based Hierarchical Federated Learning: Convergence, Group Formation, and Sampling

   https://doi.org/10.1145/3605573.3605584  

   Liu, Jiyao; Wei, Xinliang; Liu, Xuanzhang; Gao, Hongchang; Wang, Yu (August 2023, Proceedings of 52nd International Conference on Parallel Processing (ICPP 2023))